This excerpt from National Academies Press, Adding It Up: Helping Children Learn Mathematics (2001) models, in written form, the strategies that many students use as they develop procedures for adding multi-digit numbers, such as 568 + 876. Advantages are listed underneath each strategy.
Read the article "Teaching Place Value and Double Column Addition" by Constance Kamii and Linda Joseph. What are some of the insights you acquired into the advantages of student-invented procedures? Which of these is particularly salient for you and why?